Man, wouldn't it be nice to just have an infinite amount of money and you could just buy whatever you wanted? Well, unfortunately, that's not the case. We're going to be dealing with a budget and what we call a budget constraint. Let's check it out. So budget constraint, it's going to show us the limitations on what you can afford, right? The budget tells us what we can afford and not afford, right? It puts us kinda grounded on earth and says, hey, this is actually how much money you actually have, right? So we're going to be dealing with this concept of income. This is the consumer's income and it's the fixed amount of money available to spend, all right? We're going to leave the income constant as we flow through this budget constraint, right? And this income, it doesn't necessarily have to be all the money that they make, right? The income could just be the income set aside for these products, right? Or for this type of good disposable income, right? You've already paid all your other things and you have this little bit of income left over to spend on what you want, right? So this income, it's going to be this fixed amount of money available to spend. Now what we're going to do when we deal with the budget constraint, we're going to choose between various combinations of 2 goods that you can afford, right? So we're still thinking about affording these goods, but we're going to focus on 2 goods, right? We can either afford so much of one good, so much of another good or some combination of the 2. Alright? So let's dive right into our example. I think that's going to be the best way to explain this and let's see here. We've got Party Boy Paul. He spends all of his income, a whopping $18 on 2 goods, vodka and beer. So vodka sells for $6 and beer sells for $3, all right? So this is the information we need. We need his income and we need some price levels for the goods, right? We now know that information. We've got $18 and then prices of 6 and 3. So we want to complete the table and show PVP's, that's party boy Paul's budget constraint on the graph. Alright, so let's start here in the table on the right-hand side and then we'll get to the graph. So the first thing you want to do when you deal with a budget constraint, you want to know the maximum you could buy of each good. If you were only to buy that good, how much could you buy? Alright, so this almost takes us back to like pre-algebra in this case, right? Where we're told you have $18; vodka shots are $6. How many vodka shots can you afford, right? So that's the idea here. You have $18 to spend and vodka shots are $6, right? So if we take the 18 and divide it by the $6 price, well, that tells us how many vodka shots you can afford. You can afford 3 vodka shots, right? With $18 at a price of 6. How about beer? Well, the maximum amount of beer, it's going to be the same thing. If you took your $18 and divided it by the price, the price of beer being 3, right, $18 divided by 3, well you can afford 6 beers, right? 6 beers or 3 vodkas, not both, right? Because you spend all your money on vodka or all your money on beer and that's what you would get. So our formula for our maximum quantity well that's pretty easy, right? The max quantity, we just dealt with it. It's going to equal the income divided by the price. Okay? That is our maximum quantity there and that's how we solve for the maximum quantity of vodka and the maximum quantity of beers. So let's go ahead and move this information onto our graph. So notice first our axes. Our x and y axis, it's not quantity and price. We've got 2 quantities. We've got quantity on the x axis and quantity on the y axis, so we need to label which good is on which axis. We're going to put vodka up here on the y axis and beer on the x axis. Alright? It doesn't matter which is which as long as you're consistent. Okay? In this case, we're going to stick with this. We're going to do more examples using party boy Paul and we're going to leave vodka here on the y axis. Okay? So let's see. The quantity of vodka, the maximum he could get is 3 vodkas when he has 0 beer. Right? So that would be up here. He would have 3 vodkas and 0 beer and the opposite. If he had 0 vodka, he could afford 6 beers out here. That would be 6 right there. Cool. So now that we have 2 points on the budget constraint, well, it's just going to be a line. A budget constraint is just a line connecting these two points, and it couldn't be easier. We're just going to connect it, and that is our budget constraint right there. This red line, that is the budget constraint sometimes called the budget line. Okay? So the budget constraint right there. Alright, so now let's think about a few different combinations of goods, right? Because you could buy 3 vodkas and 0 beers or 6 beers and 0 vodka, but what if you wanted a little bit of both, right? Maybe some vodka and some beer. Let's think about what could happen, right? We could afford a few different things. We could afford something like say right here on our budget line, right, this combination of 2 beers and 2 vodka, that's still something affordable just like something down here. Four beers and one vodka, right? That would be something we can afford and let's just as an example, let's do this one where we have 2 beers and 2 vodka. I'm going to do it here underneath, and then we'll move on to the boxes down there. So if you had 2 beers and 2 vodka let's start with the vodka. The vodka had a price of 6, and you bought 2 of them, plus the beer having a price of 3. Whoops. Times 2. Right? You bought 2 beers also, and I'm just showing you that different points along the budget constraint are also affordable, right, as we move along the line. So $6 times 2, that's 12. 3 times 2 is 6. That's $18, right? So that's still within his budget. He's using all his income, right? And we'll notice that when we're on the budget constraint, when we're on that line, that's when we're using all our income, okay? When we're on the line, we're using all our income, but now let's think about something like this. What if we were in a situation where we bought just one beer and 1 vodka. Right? If we bought 1 beer and 1 vodka, well, that would still be affordable. Right? That's still affordable to Party Boy Paul here. One beer and one vodka. Let's see what the price would be. Well, one vodka would run him $6, one beer would run him $3, so that would be $9, right? That's affordable to him. He can have he has up to $18 but he only spent 9 in that case. Alright, so that is affordable. Compare that to something unaffordable. Let's say something like this where he's got 4 beers and 4 vodkas out here, right? That price way out there. Well, what happens there? If we've got 4 vodka and 4 beer, well, now we've got a price of $6 times the 4 vodka plus a price of $3 times the 4 beers. Right? This is 24. This is 12, we end up with $36, and he doesn't have $36 to spend. That's unaffordable to him. So what

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# Budget Constraint - Online Tutor, Practice Problems & Exam Prep

Understanding budget constraints is essential in economics, as they illustrate the limitations of consumer spending based on fixed income. When income increases, the budget constraint shifts outward, allowing for more goods to be purchased, while a price change affects only the quantity of that specific good. The maximum quantity of a good can be calculated using the formula: $\mathrm{Maximum\; Quantity}=\mathrm{Income}/\mathrm{Price}$. This framework helps analyze consumer choices and the impact of economic factors on purchasing power.

### Budget Constraint (Budget Line)

#### Video transcript

The Amazing Andy spends all of his $1,200 income on magic tricks. If card tricks cost $50 and wand tricks cost $300, which of the following consumption bundles lies upon Amazing Andy's budget constraint?

### Budget Constraint:Change in Income

#### Video transcript

Now let's see how a change in income can affect the budget constraint. So we can imagine if we make more or less money, it's going to affect the budget constraint line. So if our income increases, it's going to shift our budget constraint outward. Okay? And if it decreases, it's going to shift inward and by that I mean closer to the origin or further, right? Outward would be further away from the origin, inward would be closer to the origin. Okay? So let's see an example here where party boy Paul from our previous example, he's going to spend all of his income, which is now $24 so it increased. Previously, we had an income of $18 and now we're going to say that we have 24 instead. Everything else is going to hold constant. Vodka still sells for 6, beer still sells for 3, but he has $24 to spend now. Alright?

So the first thing I want to do real quick is I'm going to go ahead and I'm going to put our original budget constraint. If you remember, when he had $18 his budget constraint looks something like this from the previous page. 3 and 6, so he had a budget constraint something like that. Okay, this was when income so this was income whoops, income of $18 right? So that was the previous budget constraint. Let's see what happens to it now with more income. So we're going to still have quantity of vodka up here, quantity of beer on this axis and we already know our maximum quantity formula, but I wanted to reiterate it here so you guys remember.

Our maximum quantity formula that is going to be our income divided by our price, right? So let's say, what is going to be our maximum quantity of vodka? Well, the maximum quantity, we're going to take our income of 24 divided by our price of $6 for vodka. So 246, that is going to give us, not in dollars in quantity, we could buy 4 vodkas. Right? We could buy 4 vodkas. How about beer? So beer, we still have $24 but the price is 3 for beer, so we can buy 8 beers, right? With $24 So notice we were able to buy more of each good, right? Before we could only afford up to 3 vodkas, now we can afford up to 4, and before we can only afford up to 6 beers and now we can afford 8.

So let's go ahead and graph this one in blue. I'm going to graph this one in blue. So we're going to mark our axes here. We have our 4 vodkas with 0 beer and we have our 8 beers with 0 vodka, right? This is 8 over here. So what happens? We just have to connect these lines, right? To connect these points and make a new budget constraint and notice what has happened. It has shifted outward, right? It shifted further from the origin because income increased, right? And that's what we set up here. When income increases, it's going to shift outward and that's what we see here. This is his new income of 24. We have this shift outward and it shifts on both axes, right? We can buy more vodka and also more beer. We have more availability, more money to buy both products. Cool? Alright. So that's what happens when we have a change in income. Let's go ahead and pause here and move on to the next video.

An increase in income will:

### Budget Constraint:Change in Price of a Good

#### Video transcript

So now let's see how the change in the price of a good can affect the budget constraint. So we're going to see if the price of a good changes, well then the maximum quantity, the maximum quantity for only that good shifts. Okay? So we're going to move only that good. The other good is going to remain unaffected, right? We can still afford just as much as we could before of the other good, we can just afford a different amount of this good. So if the price increases, well it's going to shift downward, right? We're not going to be able to afford as much if the price goes up, but if the price goes down, it's going to shift upward and we'll be able to afford more of that good. So let's go to our example again and let's see what happens here.

Party boy Paul spends all of his income, $24 on 2 goods, vodka and beer, right? So he's got $24 in income. Let me scroll up, and the price of vodka is still $6, but the price of beer went up to $4, right? It was $3 before, now beers are $4. So this is going to affect his budget constraint, quantity of beer, and just so we remember, I'm going to graph our previous budget constraint when we had a price of $3, right? So our income was $24, but the price was $3. Well, we were able to afford 8 beers in that case or 4 vodkas, right, and we had a budget constraint that looked like this. This was our original budget constraint before this price change, right? So this was when, I'm going to put when beer was $3, right? That was when we had that budget line.

So now let's see what happens with our new price of $4. So remember, we're just going to do it again. The maximum quantity formula, that's when we take the income divided by the price. That's going to tell us the most we can afford of one of the goods. So let's start here with vodka. This isn't going to change, right? The price didn't change of vodka, the amount of income didn't change, so we're still going to have the $24 divided by the $6 per vodka, and we can afford 4 vodkas, right? But beer, there was a price change, right? So we still have $24 in income, but instead of a $3 price, we've got to divide by $4. We're going to see that we can only afford 6 beers now. We can only afford 6 beers. We can go ahead and graph this, right? We've done the hard work already, so we know that the 4 vodkas would be here and notice that it doesnâ€™t change. That dot is right on top of the previous dot, but now we can only afford 6 beers, right? So we're going to have this steeper decrease right here, and what does that tell us? Notice that the slope has changed, right? The slope when we were dealing with an income change, they were parallel. The slope didn't change, but here the slope is now kind of teetering. It's rotating around that point because we can afford less of one product but not the other product. Okay? So that's how a change in price is going to affect, is where we're going to see it holding constant on one point and rotating. Of course, if it was vodka that changed price, then the beer would be the one holding constant and then the vodka would be shifting up or down. Alright? So there you go. Let's go ahead and pause here and move on to the next video.

A change in the price of one good will:

A consumption bundle inside the budget line

Lil Kiddo just got $10 for his allowance. He has big dreams for that money and plans to buy out the toy store, slapping down the tenner at the cash register. Disillusioned, he decides to buy pogs for $0.50 each and action figures for $2 each. Which consumption bundle is unaffordable to Lil Kiddo?

Campin' Sam buys firewood and ice. When the price of firewood decreases, the maximum number of firewood she can purchase _____________ and the maximum number of ice she can purchase _______________

### Hereâ€™s what students ask on this topic:

What is a budget constraint in microeconomics?

A budget constraint in microeconomics represents the combinations of goods and services that a consumer can purchase given their income and the prices of those goods and services. It illustrates the trade-offs a consumer faces when deciding how to allocate their limited resources. The budget constraint is typically depicted as a straight line on a graph where the x-axis and y-axis represent the quantities of two different goods. The slope of the line is determined by the relative prices of the goods, and the position of the line is determined by the consumer's income.

How does a change in income affect the budget constraint?

A change in income affects the budget constraint by shifting it either outward or inward. If a consumer's income increases, the budget constraint shifts outward, allowing the consumer to afford more of both goods. Conversely, if the income decreases, the budget constraint shifts inward, reducing the quantities of goods the consumer can afford. This shift occurs because the maximum quantity of each good that can be purchased is directly proportional to the consumer's income.

How do you calculate the maximum quantity of a good a consumer can buy?

The maximum quantity of a good a consumer can buy is calculated using the formula:

$\mathrm{Maximum}\mathrm{Quantity}=\frac{\mathrm{Income}}{\mathrm{Price}}$

This formula divides the consumer's total income by the price of the good. For example, if a consumer has $24 and the price of a good is $6, the maximum quantity they can buy is:

$\frac{24}{6}=4$

Thus, the consumer can buy up to 4 units of the good.

What happens to the budget constraint when the price of a good changes?

When the price of a good changes, the budget constraint rotates around the intercept of the other good. If the price of the good increases, the budget constraint shifts inward for that good, indicating that the consumer can afford less of it. Conversely, if the price decreases, the budget constraint shifts outward for that good, allowing the consumer to afford more. The maximum quantity of the other good remains unaffected, as its price has not changed.

What is the significance of the slope of the budget constraint?

The slope of the budget constraint represents the rate at which a consumer can trade one good for another while staying within their budget. It is determined by the relative prices of the two goods. Mathematically, the slope is given by:

$-\frac{P{1}_{}}{P{2}_{}}$

where $P{1}_{}$ and $P{2}_{}$ are the prices of goods 1 and 2, respectively. A steeper slope indicates a higher opportunity cost of one good in terms of the other.